Advanced Particle Physics: Leptons and Quarks
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Questions and Answers

What is the primary focus of the research presented in the document?

  • The properties of gravitational waves
  • The mechanism of dark matter interactions
  • The history of particle physics development
  • Explaining the mass ratios of leptons and quarks (correct)

    • What challenge does the research address regarding Yukawa couplings?

  • Their independence from the Higgs VEV
  • Their relation to the speed of light
  • Their arbitrary nature in the Standard Model Higgs mechanism (correct)
  • Their experimental verification in particle collisions

    • How many generations or families of leptons and quarks are discussed in the document?

  • One
  • Two
  • Four
  • Three (correct)

    • What phenomenon is responsible for mass generation of W and Z gauge bosons according to the Standard Model?

    <p>Electroweak symmetry breaking</p> Signup and view all the answers

    What is proposed in the document concerning neutrino mass eigenstates?

    <p>Predictions for all three left-chiral mass eigenstates</p> Signup and view all the answers

    What is one reason for the existence of three generations of particles?

    <p>They arise from symmetries in the equations.</p> Signup and view all the answers

    How does the new equation discussed differ from the Koide formula?

    <p>It does not treat particle masses as constants.</p> Signup and view all the answers

    What is one application of the new equation proposed?

    <p>In the U(1)B−L symmetry framework.</p> Signup and view all the answers

    What does the new equation successfully predict regarding neutrinos?

    <p>The mass eigenstates of all three left-handed neutrinos.</p> Signup and view all the answers

    Why are the masses of up and down quarks significant?

    <p>Their masses were previously explained but now are understood under new frameworks.</p> Signup and view all the answers

    What does the quantum number ng represent?

    <p>Number of generations or families</p> Signup and view all the answers

    Which variable is used to represent the fermion spin quantum number?

    <p>S</p> Signup and view all the answers

    What is the equation used to define the quantum number nYw?

    <p>nYw = [(2 ∙ T3 − Qe) + Yw ∙ αG(Q)] / (B − L)</p> Signup and view all the answers

    What approximation is made regarding the gravitational coupling αG(Q) for most particles?

    <p>It is approximated to zero</p> Signup and view all the answers

    Which of the following particles has a non-zero value for the gravitational coupling αG(Q)?

    <p>Right-handed neutrinos</p> Signup and view all the answers

    In the equation for nYw, what do the variables B and L respectively represent?

    <p>Baryon number and lepton number</p> Signup and view all the answers

    What is the reciprocal Fibonacci constant represented by in the context?

    <p>Ψ</p> Signup and view all the answers

    Which of the following is true about the quantum number п?

    <p>It includes unstable particles and their anti-particles</p> Signup and view all the answers

    What is the lepton quantum number for all leptons?

    <p>1</p> Signup and view all the answers

    What weak hypercharge do all left-chiral leptons have?

    <p>−1</p> Signup and view all the answers

    What is the charge quantum number for charged leptons?

    <p>−1</p> Signup and view all the answers

    Which type of leptons have a weak isospin T3 = −1/2?

    <p>Left-chiral charged leptons</p> Signup and view all the answers

    What is the weak hypercharge of right-chiral charged leptons?

    <p>−2</p> Signup and view all the answers

    Which type of leptons have no weak isospin or weak hypercharge?

    <p>Right-chiral neutrinos</p> Signup and view all the answers

    In the provided equations, what does Qe represent?

    <p>Charge quantum number</p> Signup and view all the answers

    Which equation defines c4 in relation to Qe and other variables?

    <p>$c4 = \frac{2 \cdot Qe \cdot S [Qe + (B + L)]}{(B - L)}$</p> Signup and view all the answers

    What does the value of $\alpha(Q)$ depend on according to the neutrino equation?

    <p>The generation/family number N of neutrinos</p> Signup and view all the answers

    What is the experimental upper limit for the sum of all three neutrino mass eigenstates?

    <p>0.09 eV ∙ c−2</p> Signup and view all the answers

    Which statement is true regarding the mass hierarchy of left-handed neutrinos?

    <p>They have an inverse mass hierarchy.</p> Signup and view all the answers

    In the context of neutrinos, what does the equation state regarding anti-neutrinos?

    <p>They have the same Yukawa couplings and masses as neutrinos.</p> Signup and view all the answers

    What is stated about right-chiral neutrinos in relation to their existence?

    <p>They are sterile if they exist.</p> Signup and view all the answers

    What is mentioned regarding the mass of right-chiral neutrinos?

    <p>They have a colossal mass.</p> Signup and view all the answers

    What does the neutrino equation imply about the masses of neutrinos?

    <p>Neutrino masses depend on their respective generation/family number.</p> Signup and view all the answers

    Why does the variable $\alpha_G(Q)$ not need to be calculated?

    <p>It is not equal to zero or very close to zero.</p> Signup and view all the answers

    What is the charge quantum number for up-type quarks?

    <p>2/3</p> Signup and view all the answers

    What weak isospin value do right-handed d-type quarks have?

    <p>0</p> Signup and view all the answers

    In the formula for up quarks, what does the term sin²θW(Mu) represent?

    <p>The Weinberg angle for up quarks</p> Signup and view all the answers

    What is the primary characteristic of all u-type quarks compared to their anti-particles?

    <p>They have opposite charge quantum numbers.</p> Signup and view all the answers

    What is the value of weak isospin T3 for left-handed d-type quarks?

    <p>1/2</p> Signup and view all the answers

    How is the value of α for up quarks estimated in the formula?

    <p>α is approximated as α(mu).</p> Signup and view all the answers

    Which quark parameter includes the term 6π in its formula?

    <p>The Yukawa coupling</p> Signup and view all the answers

    What does the value for MN represent in the context of quarks?

    <p>The mass of quarks</p> Signup and view all the answers

    Study Notes

    Explaining Ratios of Masses of Leptons and Quarks

    • Three generations or families of leptons and quarks exist.
    • The known mass ratios of these particles within their generations are explained.
    • The article attempts to solve the problem of Yukawa couplings as arbitrary parameters in the Standard Model Higgs mechanism.
    • A new methodology based on the running of the fine-structure constant, quantum numbers, and the Weinberg angle is introduced to explain Yukawa couplings of all leptons and quarks.
    • Predictions are made for left-chiral neutrino mass eigenstates.
    • Upper limits are provided for right-chiral neutrino mass eigenstates.

    Standard Model Scalar Potential

    • The Standard Model scalar potential is given by V(Φ) = m²Φ†Φ + λ(Φ†Φ)² where:
      • Φ is a self-interacting SU(2) complex doublet.
      • Y = 1 (weak hypercharge)
      • V(Φ) is the most general renormalizable scalar potential.
      • A negative quadratic term results in a non-zero vacuum expectation value (v).
      • v ≈ 246.22 GeV.
      • GF is the Fermi coupling constant

    Higgs Lagrangian

    • The Higgs Lagrangian relates the Higgs field to gauge fields (Wμ and Bμ).
    • g and g' represent SU(2)₁ and U(1)y gauge couplings.
    • The Lagrangian includes the covariant derivative and potential terms.

    Yukawa Lagrangian

    • Lepton masses are defined by a free parameter (Yukawa Coupling af).
    • The Higgs field couples with fermions with a Yukawa coupling defined.
    • The Higgs mechanism does not predict fermion masses directly.

    Higgs-Yukawa Family/Generation Equation

    • A new equation for Yukawa couplings is introduced.
    • It doesn't depend on the Higgs VEV and explains mass ratios of the three generations.
    • The equation is presented:
      • It involves the running fine-structure constant (a(Q)).
      • N representing generation number.
      • θw(Q) representing the running Weinberg angle.
      • (1 + Δqf) is the correction factor for unstable leptons.
      • It includes the quantum numbers and fermion flavour.

    Leptonic Solutions

    • All leptons have a lepton quantum number (L).
    • Left-chiral leptons have a weak hypercharge (Yw = -1) while right-chiral, charged leptons have a hypercharge of -2.
    • Right-chiral neutrinos are "sterile," lacking weak hypercharge, weak isospin, and charge.

    Charged Leptons

    • All charged leptons have a charge quantum number (Qe).
    • Left-chirality has weak isospin (T3 = 1/2).
    • Right-handed charged leptons have zero weak isospin.
    • Formula for electron, muon, and tau Yukawa couplings are shown.

    Neutrino Solutions

    • All neutrinos have a charge of 0.
    • Left-chiral neutrinos have weak isospin (T3 = 1/2).
    • Right-handed, or sterile neutrinos (if present) have weak isospin = 0 and do not have charge.
    • Two formulae are presented for Left and Right neutrinos with their predictions of masses.

    Quark Solutions

    • Quarks have a baryon quantum number (B = 1/3 or -1/3 ).
    • Up-type quarks have weak hypercharge (Yw = 1/3), while down-type have (Yw = -2/3).
    • Formulas for down (d), strange (s), bottom (b) and up (u), charm (c), top(t) type quark Yukawa couplings and masses are presented with their respective quantum numbers.

    References

    • Citations to numerous Physics publications and articles.

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    Explaining Ratios of Lepton & Quark Masses (PDF)

    Description

    Explore the intricate relationships between the mass ratios of leptons and quarks in this advanced quiz. Delve into the complexities of the Standard Model's Higgs mechanism and the Yukawa couplings. Test your knowledge on key concepts such as the scalar potential and predictions for neutrino mass eigenstates.

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